One-pass batching algorithms for the one-machine problem
Discrete Applied Mathematics
Scheduling Algorithms
Batching and scheduling in a multi-machine flow shop
Journal of Scheduling
Single machine scheduling with batch-dependent setup times
Information Processing Letters
Minimizing flow-time on a single machine with integer batch sizes
Operations Research Letters
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A flow-shop batching problem with consistent batches is considered in which the processing times of all jobs on each machine are equal to p and all batch set-up times are equal to s. In such a problem, one has to partition the set of jobs into batches and to schedule the batches on each machine. The processing time of a batch B i is the sum of processing times of operations in B i and the earliest start of B i on a machine is the finishing time of B i on the previous machine plus the set-up time s. Cheng et al. (Naval Research Logistics 47:128---144, 2000) provided an O(n) pseudopolynomial-time algorithm for solving the special case of the problem with two machines. Mosheiov and Oron (European Journal of Operational Research 161:285---291, 2005) developed an algorithm of the same time complexity for the general case with more than two machines. Ng and Kovalyov (Journal of Scheduling 10:353---364, 2007) improved the pseudopolynomial complexity to $O(\sqrt{n})$ . In this paper, we provide a polynomial-time algorithm of time complexity O(log驴3 n).